It's more like 150 years, but weddings have gotten much more formal and formalized in that timeframe. Of course, plenty of people have informal/courthouse/Vegas weddings, but the idea of a wedding has changed from a small gathering of family and close friends in the home of the bride's or groom's parents to a large, fancy, ceremonial affair.

In 1840, Queen Victoria of Great Britain married Prince Albert. The bride wore a white satin dress, which immediately set the standard for brides-to-be who could afford white material and had the means to keep it clean. Prior to that (and for many years following for most women), women were typically married in their "best" dress, which was often made of a dark material so it could double as a funeral dress for those occasions. The rise of a (White) middle class in the United States meant that more women could aspire to the trappings of wealth, such as a big fancy white dress, catered dinner, a confectioner-made (rather than homemade) cake, engraved invitations, and such. Professions arose or adapted to meet these needs - florists, caterers, etc. Much of the modern wedding industry is based on this desire to imitate the formality and wealth the rich and aristocratic displayed on a daily (or at least frequent) basis -- allowing the bride and groom to be "rich for a day." (As someone who studies the history of media and technology, I have to point out here the influence of the invention of photography and the spread of newspapers, whose "society pages" helped circulate images of wealth widely.)

If you are interested in reading more, Carol Wallace's All Dressed in White: The Irresistible Rise of the American Wedding (Penguin, 2004) is a pop history of weddings in the U.S.

Resumes have become an institution in the last 75 or so years. It used to be you carried a note from a Lord or trade guild and that was about it. These days people agonize over small details because these trivial things seem to mater. You will not find a lot of historical examples of resumes since they were almost unheard of.

http://www.lettersofnote.com/2012/03/skills-of-da-vinci.html?m=1

There is an interesting set of arguments about this from a sociological standpoint, one of which I am familiar with is by Samus Khan in Privilege (/u/yodatsracist can chime in to clarify and correct me). Basically, going back to Bourdieu what we call using the shorthand term "formal" is really a set of behavioral norms, or to put it another way, embodied class knowledge. The way you behave is the way you communicate your social position in a largely unconscious process: using the right fork, properly tying a bow tie, using a pocket square all communicate one aspect of social position; being able to fix a car or crush a beer can on your forehead communicates a different one. If these seem stereotypical, well, that is because they are: stereotypes are how we "read" the information communicated by behavioral norms. The argument is a lot more complicated than that, but that should be a serviceable overview.

The stuffy formalism of the nineteenth and early twentieth century is essentially a result of the class position of the social elite. Unlike the earlier hereditary nobility, the capitalist elite was undergirt by a meritocratic ideology, so they justified their position by essentially saying they earned it or at least actively contributed to it, rather than the earlier elite who viewed it as an essential aspect of their very being. John Blackwell, factory owner, needed to constantly reinforce his status position in a way that Guy de la Mantoyet, Baronet of Lancashire did not. So the demands of a young, somewhat mobile elite required a far more regulated set of behavioral norms than a hereditary one. If you compare George Washington's etiquette book with later Victorian ones, for example, it is far more concerned with having correct class knowledge (who is who, how to act to who) than with the sort of obsessive physical purity of the latter. Now this arguments gets a lot more complicated, but again, this should be serviceable.

Now the interesting thing that has happened in the last fifty odd years is that the earlier ideology has been replaced by a more radically egalitarian one (even as social mobility has actually decreased--ideology need not be reality!). For a whole variety of reasons, including the decline of wealth based on "pure" capitalism in favor of high status wage labor, the sort of obsessive behavior regulation has become untenable unstable. What replaced it is a sort of cultural omnivorousness: if an elite in 1900 was able to deeply appreciate opera and knew how to formally dine like second nature, the elite of 2000 could listen to classical, jazz, and hip hop, and could dine formally and use chopsticks at a hole in the wall noodle joint. Instead of communicating status by deep behavioral embodiment of a set of norms, they are able to freely "code switch" depending on the situation.

So in a way, American culture didn't actually become less formal if by formal we mean status embodiment, Just that the needs of high status and thus the norms of embodiment have changed.

I'm curious about whether this is a trend that occurs in other countries or past cultures as well. Could it be a result of the Internet and other increased forms of communication? Maybe accessibility breeds familiarity.

Please don't delete or ban if I'm breaking rules here.

Followup: Also, how formal was the past in reality, and how much of our perception is simply romanticization in modern media that may not reflect reality?

Also, if I could ask a related question, are there examples of American culture becoming more formal at times? For example, I am dimly aware of soldiers during the Civil War espousing an old-school chivalry in letters, and of the "Victorian" era in general being formal and dour; but I don't know enough to assess either if these are correct understandings or to compare them with prior time periods.

I would say the process of getting a job has become dramatically more formalized. When I was very young it was already becoming rare but you would still once in a while be able to pick up a job on the spot by talking to someone in charge. It has been more than 10 years since anyone I know in person has been able to land any kind of work without having to submit resume's and formally interview for even the most bullshit of little jobs.

Could this question be extended over Western culture as a whole? In fact, are there any cultures that have not become less formal over the last century?

Adoption has become a more formal process. Orphaned children used to ride on trains, getting off at each station where farmers would look them over. If a child looked like they could be helpful in the home or on a farm, it was "adopted". Now, because of international adoptions, agencies are needed to guide adoptive parents through the adoption process. Also, a majority of US adoptions are now infants and toddlers. This has led to a more formal and more administrative process.

I think education has become more formal. We don't really see people taking apprenticeships anymore. And the whole college thing has blown up a lot. But even at the elementary school level, we see more structure than the Victorians had, I believe.